Like sprinting. You have a 'seeing' bar, or a 'seeing' cooldown or something. While not using this ability, the screen is black, except for UI.
Game set in a setting where all sentient individuals are blind, and "vision" is a mystic ability. Kinda lile using the force, but the majority of people can do it.
Local culture and architecture and stuff are designed around that.

You would need really good sound design for that to work. But if you really could get that level of sound design, it could be really cool.

sounds AWFUL

Some of the levels in OverCooked are like that and they're the worst ones

Reminds me of FTL. Your sensors subsystem monitors the inside of your ship, and if it gets taken out, you can't see anywhere that you don't have a crewmember, which makes dealing with on-board fires difficult, because you don't know where they are.

Maybe a game where you could use echolocation to roughly see most things, but used limited "sight" powers to notice things others can't. Maybe have it set in a cave environment where the shapes of enemies and rock formations can looks similar.

Maybe a game where the player character is the only person who can see and they have to take out big blind beasties a la assassin's creed or sniper elite.

Or you have guide allies who can't see and you're the only person who can properly guide them.
Of course it's too late to be first at the idea. From my observation Lemmings are incapable of sight, and only the player can see. It makes a lot of sense anyway.

If you want to make a game like that, step one is to find a blind person (preferably more than one) and ask for their input.

Tell them I’m handsome

Even Barney deserves to fool one person.